We consider collective emission of a single photon from a cloud of
N two-level atoms (one excited, $N\ensuremath{-}1$ ground state). For a dense cloud the problem is reduced to finding eigenfunctions and eigenvalues of an integral equation. We discuss an exact analytical solution of this many-atom problem for a spherically symmetric atomic cloud. Some eigenstates decay much faster then the single atom decay rate, while the others undergo very slow decay. We show that virtual processes yield a small effect on the evolution of rapidly decaying states. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important yielding additional decay channels which results in a slow decay of the otherwise trapped states. We also show that quantum mechanical treatment of spontaneous emission of weakly excited atomic ensemble is analogous to emission of
N classical harmonic oscillators.
We study cooperative single-photon spontaneous emission from three multilevel atoms with one of them being excited for different atomic configurations in optical vector theory. The dynamic evolution is solved by finding the eigenvalues of a 3 \ifmmode\times\else\texttimes\fi{} 3 matrix, and then the relevant decay rates and Lamb shifts are obtained analytically. It is shown that the symmetry of atomic configuration has a big influence on the super-radiance of the system. To obtain strong super-radiance requires not only the distances among the three atoms to be much shorter than the wavelength, but also to have symmetrical distribution. We also calculate the emission spectra and find that it normally has three peaks, but it has two peaks under the equilateral-triangle configuration.
We study the correlated spontaneous emission from a dense spherical cloud of N atoms uniformly excited by absorption of a single photon. We find that the decay of such a state depends on the relation between an effective Rabi frequency Omega proportional square root N and the time of photon flight through the cloud R/c. If OmegaR/c<1 the state exponentially decays with rate Omega(2)R/c and the state lifetime is greater than R/c. In the opposite limit OmegaR/c>>1, the coupled atom-radiation system oscillates between the collective Dicke state (with no photons) and the atomic ground state (with one photon) with frequency Omega while decaying at a rate c/R.
We investigate the collective spontaneous emission from an ensemble of two-level atoms evenly distributed inside a sphere with a low density. An initial symmetric single-excitation state is considered and polarizations for all atoms are assumed to be aligned in the same direction. We find that the superradiant decay rate of the ensemble exhibits oscillatory features dependent on the radius of the sphere and the atomic radiation wavelength, indicating that the collective emission rate can be less than the single-atom decay rate for certain parameters. Moreover, the system exhibits a hidden equivalence where the collective emission from the ensemble gives the same radiation rate as the case of a two-atom model where one atom is at the center of the sphere and the other effective large atom, composed of all other atoms, is localized at the edge of the sphere along the polarization direction. Our result hence provides a potential method towards exploring complex many-body physics by simplifying the model into a two-body problem.
The cooperative spontaneous emission by a fully inverted array of N atoms, interacting with and via the radiation field is studied. The arrays to which this treatment is applicable are symmetric under the exchange of any pair of atoms, including the dipole-dipole interaction in the energy and are confined to a volume with linear dimensions that are small relative to the radiation wavelength. Analytic expressions are obtained for the populations of the levels and the intensity of emission as functions of time, and for the spectrum of the radiation emitted in the cascade to the ground state.
We investigate the properties of the cooperative decay modes of a cold atomic cloud, characterized by a Gaussian distribution in three dimensions, initially excited by a laser in the linear regime. We study the properties of the decay rate matrix
S, whose dimension coincides with the number of atoms in the cloud, in order to get a deeper insight into properties of cooperative photon emission. Since the atomic positions are random,
S is a Euclidean random matrix whose entries are a function of the atom distances. We show that in the limit of a large number of atoms in the cloud, the eigenvalue distribution of
S depends on a single parameter
b0, called the cooperativeness parameter, which can be viewed as a quantifier of the number of atoms that are coherently involved in an emission process. For very small values of
b0, we find that the limit eigenvalue density is approximately triangular. We also study the nearest-neighbor spacing distribution and the eigenvector statistics, finding that although the decay rate matrices are Euclidean, the bulk of their spectra mostly behaves according to the expectations of classical random matrix theory. In particular, in the bulk, there is level repulsion and the eigenvectors are delocalized, therefore exhibiting the universal behavior of chaotic quantum systems.